Fair Division

From Cake-Cutting to Dispute Resolution

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Paperback | 6 May 1996

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288 Pages

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Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair Division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or 'bads' like chores), or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, 'I cut, you choose', the authors show how it has been adapted in a number of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular they focus on procedures which provide 'envy-free' allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures.

Industry Reviews

'In this remarkable book, Brams and Taylor bring to the attention of social scientists a literature thus far confined to puzzle-solving and other mathematical magazines. The book's emphasis on Envy-Freeness will please economists; numerous practical mechanisms for negotiation will appeal to the political scientist and the lawyer; finally, Brams and Taylor's original fair division procedures are of interest to all researchers.' Herve Moulin, Duke University '... explains everything a layperson might need to know about fair division ... lawyers should love the book'. Discover

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List of figures	p. xii
List of tables	p. xiii
Acknowledgments	p. xiv
Introduction	p. 1
Proportionality for n = 2	p. 6
Biblical origins	p. 6
Divide-and-choose and applications	p. 8
Filter-and-choose and applications	p. 12
The role of information	p. 16
Austin's moving-knife procedure and applications	p. 22
Proportionality for n ] 2: the divisible case	p. 30
Introduction	p. 30
The Steinhaus-Kuhn lone-divider procedure	p. 31
The Banach-Knaster last-diminisher procedure	p. 35
The Dubins-Spanier moving-knife procedure	p. 36
Applications of last-diminisher and its moving-knife version	p. 38
The Fink lone-chooser procedure	p. 40
Woodall's and Austin's extensions of Fink's procedure	p. 41
Efficiency, entitlements, and chores	p. 44
Proportionality for n ] 2: the indivisible case	p. 51
Introduction	p. 51
Knaster's procedure of sealed bids	p. 52
Lucas' method of markers	p. 57
Efficiency and entitlements	p. 62
Envy-freeness and equitability for n = 2	p. 65
Introduction	p. 65
Bargaining and fair division	p. 66
The Adjusted-Winner (AW) procedure	p. 68
The Proportional-Allocation (PA) procedure	p. 75
The combined procedure	p. 78
Three or more players	p. 80
Conclusions	p. 83
Appendix	p. 85
Applications of the point-allocation procedures	p. 95
Introduction	p. 95
The Panama Canal treaty negotiations	p. 95
A hypothetical divorce settlement	p. 98
A real divorce settlement	p. 102
AW versus Knaster's procedure	p. 108
Conclusions	p. 113
Envy-free procedures for n = 3 and n = 4	p. 115
Introduction	p. 115
The Selfridge-Conway discrete procedure	p. 116
The Stromquist moving-knife procedure	p. 120
The Levmore-Cook moving-knife procedure	p. 122
The Webb moving-knife procedure	p. 124
Two other moving-knife procedures for n = 3	p. 125
A four-person moving-knife procedure	p. 126
Envy-free procedures for arbitrary n	p. 129
Introduction	p. 129
Two approximate procedures	p. 130
An infinite procedure	p. 133
A finite procedure	p. 138
Applying the trimming procedure to indivisible goods	p. 143
Efficiency, entitlements, and chores	p. 148
Appendix	p. 156
Divide-the-dollar	p. 158
Introduction	p. 158
DD1: a reasonable payoff scheme	p. 160
DD2: adding a second stage	p. 163
DD3: combining DD1 and DD2	p. 168
The solutions with entitlements	p. 170
Conclusions	p. 173
Appendix	p. 174
Fair division by auctions	p. 178
Introduction	p. 178
Two-stage auctions	p. 181
Two-stage auctions: the private-value case	p. 183
One-stage common-value auctions: the winner's curse	p. 188
Two-stage auctions: the common-value case	p. 191
Conclusions	p. 198
Appendix	p. 201
Fair division by elections	p. 204
Introduction	p. 204
The Hare system of single transferable vote (STV)	p. 206
The Borda count	p. 209
Cumulative voting	p. 212
Additional-member systems	p. 213
Controlled roundings	p. 216
Further narrowing: the search may be futile	p. 219
Constrained approval voting (CAV)	p. 225
Conclusions	p. 228
Conclusions	p. 231
Glossary	p. 237
Bibliography	p. 248
Index	p. 264
Table of Contents provided by Syndetics. All Rights Reserved.

Fair Division

From Cake-Cutting to Dispute Resolution

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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